Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

Effect of rare-earth oxides on the magnetic properties of anisotropic barium ferrites

The effect of rare-earth oxides on the properties of anisotropic barium ferrites has been studied by x-ray structural and Mössbauer methods. Additions of SrCO₃, as well as SrCO₃ and La₂O₃, SrCO₃ and Pr₆O₁₁, SrCO₃ and Nd₂O₃, SrCO₃ and Sm₂O₃ in amounts of 7.5 mole % Sr and 10 mole % rare-earth element to grade-A barium powder results in the substitution of barium ions by Sr and rare-earth ions; consequently, the energy of magnetic anisotropy changes and the technically important parameters B_r and (BH)_max increase.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 34–39, January, 1989.     

An algebra of meromorphic corner symbols

Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.     

Roles of rhenium diimine complexes as metal‐ion probes and photosensitizers in functional polyurethanes

Polyurethanes incorporated with rhenium diimine complexes were synthesized. The polymers exhibited interesting morphologies and solution properties. Results from gel permeation chromatography suggested the formation of polymer aggregates in solutions. The polymers could act as probes for metal ions. The addition of metal ions to polymer solutions led to significant changes in the electronic absorption properties of the polymer solutions. This was attributed to the interactions between the polyether moieties and metal ions. The metal complexes could also act as efficient photosensitizers. After doping with charge‐transport viologens, the photoconductivity of the polymers was greatly enhanced. The experimental quantum efficiency was simulated with Onsager's theory. The thermalization distances and the primary yields were typically 12–14 Å and 10^?3, respectively. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1708–1715, 2003     

Two-Variable Identities in Groups and Lie Algebras

We study two-variable Engel-like relations and identities characterizing finite-dimensional solvable Lie algebras and, conjecturally, finite solvable groups and introduce some invariants of finite groups associated with such relations. Bibliography: 29 titles.     

A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

Banana-shaped mesogens: a new homologous series of compounds exhibiting the B7 mesophase

The synthesis and characterization of a new homologous series of compounds, the 2-cyano-1,3-phenylene bis[4-(4-n-alkoxyphenyliminomethyl)benzoates] derived from 2-cyanoresorcinol is reported. All the compounds are enantiotropic mesogens and exhibit the fascinating B₇ mesophase. The characterization of the mesophase was performed using polarizing optical microscopy, differential scanning calorimetry, X-ray diffraction and electro-optical studies.     

Decay of neutron-rich Ga isotopes near N = 50 at PARRNe

The PARRNe facility has been used to produce neutron-rich isotopes ^83,84Gaby the ISOL method. Their decay has been studied, and β-γ coincidence and γ-γ coincidence data were collected as a function of time. The first two excited levels in ⁸³Ge and the first excited level in ⁸⁴Ge have been measured for the first time.     

Fixed points in the family of convex representations of a maximal monotone operator

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exists a convex representation of the operator which is a fixed point of this conjugation.

     

The role of As2O3 on the stability and some physical properties of PbO-Sb2O3 glasses

PbO-Sb₂O₃ glasses added with different concentrations of As₂O₃ (10-55 mol%) were prepared to understand their IR spectra, elastic properties (Young's modulus E, Shear modulus G, microhardness H), optical absorption and dielectric properties (constant ε, loss tan δ, ac conductivity σ_ac over a moderately wide range of frequency and temperature and breakdown strength in air medium at room temperature). Results have indicated that the structure of the PbO-Sb₂O₃-As₂O₃ glass is more rigid when the concentration of As₂O₃ is around 40 mol%.